Question 8

A sphere of mass M, radius r, and rotational inertia I is released from rest at the top of an inclined plane of height h as shown above.

Conservation of Energy - mv Kroc = 210 vcm= ro We now can consider the kinetic energy in two parts, rotation and translation -Mv2cm+}1 of the center of mass. Then Mgh = MVcm + 10 — Solving for vcm yields 2Mghr2

Question 17

Board Skater Top View A long board is free to slide on a sheet of frictionless ice. As shown in the top view above, a skater skates to the board and hops onto one end, causing the board to slide and rotate. In this situation, which of the following occurs? (A) Linear momentum is converted to angular (B) (C) (D (E) momentum. Kinetic energy is converted to angular momentum. Rotational kinetic energy is conserved. Translational kinetic ener is conserved. Linear momentum and angular momentum are both conserved.

  • No net external torque --> no change in angular momentum

  • No net external force --> no change in linear momentum

Question 25

25. As shown above, two students sit at opposite ends of a boat that is initially at rest. The student in the front throws a heavy ball to the student in the back. What is the motion of the boat at the time immedi- ately after the ball is thrown and, later, after the ball is caught? (Assume that air and water friction are negligible.)

  • After ball tossed it has momentum toward back so the boat must have forward momentum to maintain the zero initial momentum.

  • After the catch both the ball and boat the two must be at the same speed and this must be at rest to have momentum zero as it was originally

Question 29


  • Neither the mass, M, nor the spring constant, k, depend on the gravitational force of the planet.

Question 33


2vosin0 Time of flight, t g vä sin20 Maximum height reached, H asin20 v Horizontal range, R

The 450 angle gives the maximum horizontal travel to the original elevation, but the smaller angle causes the projectile to have a greater horizontal component of velocity, so given the additional time of travel allows such a trajectory to advance a greater horizontal distance. In other words given enough time the smaller angle of launch gives a parabola which will eventual cross the parabola of the 450 launch.

Question 34

A car travels forward with constant velocity. It goes over a small stone, which gets stuck in the groove of a tire. The initial acceleration of the stone, as it leaves the surface of the road, is (A) vertically upward orrzont y orwa (C) horizontally backward (D) zero (E) upward and forward, at approximately 450 to the horizontal

  • The path of a point on the rim of a non-slipping rolling wheel is a cycloid.


Question 35

  • Escape speed

    -11.2 km/ s escape GMm 2GM

  • Orbital speed

    GMm mv GM

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